Periodic DFT study of the tetragonal $ZrO_{2}$ nanocrystals : equilibrium morphology modeling and atomistic surface hydration thermodynamics

A thorough periodic DFT/PW91 study of water sorption (0.1 < $\Theta$ < 1) on tetragonal $ZrO_{2}$ ($P4_{2}$/nmc) nanocrystals was performed by means of the plane-wave periodic DFT calculations complemented by atomistic thermodynamics. All (101), (001), (100), (111), and (110) planes exposed by faceted t-$ZrO_{2}$ nanocrystals were taken into account, and their atomic structure, surface reconstruction, and stabilization upon water adsorption were systematically investigated and analyzed in detail. Using the calculated surface energies of the reconstructed planes, a doubly truncated tetragonal-bipyramidal shape of the tetragonal zirconia nanocrystallites in dry and wet conditions was predicted by means of the Wulff construction. The results remain in very good agreement with the experimental HR-TEM images. For each of the exposed planes, the computed changes in the free enthalpy of water adsorption under specified hydration conditions were used to construct two-dimensional surface coverage versus temperature and pressure diagrams, $\theta _{hkl} =f(T,p_{H2O})$. The preded temperature dependence of total adsorption $\Theta$(T) and d $\Theta$/dT patterns compare well with water TPD experiments. It was found that water adsorption/desorption occurs in a tri-(101), bi-(001) and (111), and a monomodal (100) way. To epitomize the overall water adsorption thermodynamics at the macroscopic scale, a multisite Langmuir and Fowler−Guggenheim isotherms were calculated and interpreted in terms of intermolecular and interfacial interactions between the adspecies and the surface.